Effects of neutron star dynamic tides on gravitational waveforms - - PowerPoint PPT Presentation

Effects of neutron star dynamic tides

• n gravitational waveforms

within the Effective One-Body approach

• A. Taracchini F. Foucart K. Hotokezaka
• A. Buonanno M. Duez K. Kyutoku
• J. Steinhoff L. E. Kidder M. Shibata
• H. P

. Pfeiffer

• M. A. Scheel
• B. Szilagyi
• C. W. Carpenter

arXiv:1602.00599

Tanja Hinderer

(University of Maryland)

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Astrophysics seminar Goethe Universität Frankfurt June 14, 2016

Overview

Motivation: potential to determine properties of ultra-dense matter using gravitational waves from NS-NS and NS-BH binaries

multimessenger studies (sGRBs, afterglows, neutrinos) sources of r-process elements

Requires robust models Recent improvements: dynamical tides during inspiral Tidal Effective One-Body model Conclusions

1

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Neutron stars (NSs)

2

strongest gravitational environment where matter can stably exist

• ther extremes of physics:

spins up to 38000 rpm, huge magnetic fields, superfluidity, superconductivity, solid crust, … 1939: theoretical prediction [Oppenheimer &

Volkoff]

1968: discovery of pulsars [Hewish, Bell,+] 1969: pulsars = neutron stars [Gold] > 2000 observed to date (~1/1000 stars) masses ≳ Msun, radii ~ 10km matter compressed to several times nuclear density

Debris from a supernova in 1054 Crab Pulsar

What is the nature of matter in such extreme conditions?

Phases of the strong force

3

H2O

[Wambach+2011] [credit: Garrido]

Neutron stars (NSs)

QCD (conjectured)

NS structure

4

deep core: ≳ 2 × 𝝇nuclear exotic states of matter? deconfined quarks? condensates?

?

crust: ~ km

• uter core: ~ few km

uniform liquid?

Theoretical difficulties: many-body problem with strong interactions unknown composition and equation of state (EoS) Experiments: properties of neutron-rich nuclei, phases of the strong force

impossible to reproduce conditions in NSs

NS global properties from microphysics

5

pressure vs. density mass vs. radius

Einstein’s field equations

composition, multi-body forces, etc., reflected in the EoS EoS determines observables (mass, radius, …)

[ Özel & Freire 2016 ]

NS radius measurements

6

Masses: to ~0.0001% from pulsar timing Radii: difficult to determine Quiescent low-mass X-ray binaries, isolated cooling NS

[image B. Rutledge]

• ther methods,

Thermonuclear X-ray bursts

[image B. Rutledge] [image: K. Gendreau]

Millisecond pulsars: X-ray pulse shape of rotating hot-spot

pulse phase relative flux

x-ray intensity vs. time relative to burst start [Galloway+2006]

Results for NS radii

systematic uncertainties: distance atmosphere size of emitting region surface composition identification of spectral features magnetic field ….

7

[Lattimer & Steiner 2014 ]

Examples of results

potentially more robust EoS measurements with gravitational waves (GWs) asymmetric rotating NSs (crust physics) coalescing binaries

Matter and energy curve space and warp time That curvature is responsible for gravity Accelerating masses generate ripples in curvature: GWs. Fractional deviation away from flat space: Carry enormous power: ≈10 51 Watts (c.f. sun radiates ≈10 26 Watts) Interact very weakly with matter. Also produced by processes in the early universe, supernova explosions, asymmetric pulsars … h ∼ G c4 ¨ I D ∼ G c4 mv2 D ∼ 10−22

Gravitational waves (GWs) in brief

8

credit: NASA

distance to source

≈ 8 × 10−45 s2

kg m

Measuring GWs with interferometers

9

L L+ΔL

suspended mirrors laser beam splitter photodetector

X

h(t)

change in intensity due to difference in phase: laser frequency extra roundtrip travel time in the arm

∆φ = 2πf 2∆L c = 4πf c h(t)L

Worldwide network of GW detectors

10

Advanced LIGO first observing run completed

~ 2019 design sensitivity

Advanced Virgo major hardware upgrade almost completed GEO 600 LIGO India ~2020 + KAGRA ~2020 + LIGO Hanford (WA)

L=4km L=4km

LIGO Livingston (LA)

GW signal from black hole (BH) binaries

11

… until they collide

Inspiral Merger/ringdown

the orbit shrinks … … velocity ~0.6 c,

• rbital period ~10 ms …

36 M⦿ 29 M⦿

… and merge into a single BH

62 M⦿

time (s)

0.3 0.35 0.4 0.45

• 1.0
• 0.5

0.5 1.0

h(t) (x10-21)

waveform

BHs: regions of extreme spacetime curvature, characterized completely by only mass & spin

GW signal from BH binaries

12

details of the waveform depend on the parameters (masses, spins, …)

equal mass, no spin unequal mass, no spin equal mass, with spins

extracting the information from the signal requires highly accurate models as templates for data analysis

courtesy A. Taracchini

Approaches to the two-body problem

13

• rbital

separation r/M

mass ratio M/𝞶

Numerical relativity

post-Newtonian theory black hole perturbation theory

Newtonian dynamics test particle limit

Torbit ∼ M ✓ r M ◆3/2

Tinspiral ∼ M ✓M µ ◆✓ r M ◆4

timescales:

Approaches to the two-body problem

13

• rbital

separation r/M

mass ratio M/𝞶

Numerical relativity

post-Newtonian theory black hole perturbation theory

Newtonian dynamics test particle limit

Torbit ∼ M ✓ r M ◆3/2

Tinspiral ∼ M ✓M µ ◆✓ r M ◆4

timescales:

LIGO band

path to merger

Approaches to the two-body problem

13

• rbital

separation r/M

mass ratio M/𝞶

Numerical relativity

post-Newtonian theory black hole perturbation theory

Newtonian dynamics test particle limit

Torbit ∼ M ✓ r M ◆3/2

Tinspiral ∼ M ✓M µ ◆✓ r M ◆4

timescales:

LIGO band

path to merger

Effective One-Body (EOB) model:

combines all information into a complete waveform model for LIGO searches

[Buonanno, Damour 1999, 2000]

radiation reaction forces factorized waveforms

Effective-One-Body (EOB) approach

MAP

ν=µ/M

effective Hamiltonian Heff Binary problem

effective spacetime effective particle

A = 1 − 2M r + ν δAPN(r; M, ν)

14

HEOB(r, pr, pφ; M, ν) = M s 1 + 2ν ✓Heff µ − 1 ◆

Hamiltonian for the dynamics:

Effective description

ds2

eff = −A(M, ν, r)dt2 + B(M, ν, r)dr2 + r2dφ2

lengthy PN description

Complete EOB waveforms

15

Evolve the two-body dynamics up to the light ring (spherical photon orbit) Smooth transition Ringdown: quasinormal modes (QNM) of final BH

inspiral ringdown

waveform GW frequency

least damped QNM frequ.

superposition

• f QNMs

Calibrated

EOB

numerical relativity

m1=m2, S1=S2=0.98 Smax

58 56 57 59 60 61 62 6364 0.3 58 56 57 59 60 61 62 6364

Calibrated

58 56 57 59 60 61 62 6364

56 57 58 59 60 61 62 64 56 57 58 59 60 61 62 64

GW cycles GW cycles

Performance of EOB waveforms

16

[courtesy A. Taracchini] [Taracchini+ 2016]

no tuning tuned

recent extension to precessing spins

GW150914 detected by LIGO

17

[LSC 2016]

The importance of models for GW150914

18

2σ 3σ 4σ 5.1σ > 5.1σ 2σ 3σ 4σ 5.1σ > 5.1σ

8 10 12 14 16 18 20 22 24

Detection statistic ˆ ρc

10−8 10−7 10−6 10−5 10−4 10−3 10−2 10−1 100 101 102

Number of events

GW150914 Search Result Search Background Background excluding GW150914

establish >5σ detection significance perform tests of general relativity

[LSC 2016]

measure source properties

Experimental progress

19

credit: atlasoftheuniverse

LIGO’s visible volume of the universe for GWs from double neutron stars:

initial LIGO

Advanced LIGO: first observing run

design goal: ~ 1 million galaxies

GW signal from NS-NS binaries

20

[data from T. Dietrich]

collapse to BH

≈ point-masses NS NS tidal effects last ~ 20 cycles

merger post-merger

NS-NS BH-BH >103 GW cycles rich characteristic frequency spectrum > kHz

GW signal from NS-BH binaries

21

tidal effects ≈ point-masses NS

BH

tidal disruption

• r plunge

GW shutoff can be in aLIGO band larger modeling uncertainty in point-mass GWs than for NS-NS

[data from F. Foucart]

small ∼

1 (1 + q)5

q = mBH mNS

NS-BH BH - BH

QNS = −λ Etidal

Tidal effects during inspiral

22

tidal deformability induced quadrupole companion’s tidal field

dominant effect:

pressure - density

credit: B. Lackey

λ- mass

Einstein’s Eqs: linear perturbations to equilibrium sol. [One 2nd order ODE]

Love number

λ = 2 3k2R5

NS radius

Influence on the GWs

23

Energy goes into deforming the NS moving tidal bulges contribute to gravitational radiation GW phase from energy balance:

tidal contribution:

[ Flanagan & TH 2008, Vines+ 2011]

E ∼ Eorbit − 1

4QNSEtidal

˙ EGW ∼ h

d3 dt3 (Qorbit + QNS)

i2

dφGW dt = 2Ω, dΩ dt = ˙ EGW dE/dΩ

∆φtidal

GW ∼ λ(v/c)10

M 5

QNS = λ Etidal

Influence on the GW phase

24

Tidal phase contribution in the stationary phase approx. : most sensitive to the weighted average: for identical NSs:

δ˜ Λ = 0

ψtidal = 3 128νx5/2  − 39 2 ˜ Λx5 + ✓ − 3115 64 ˜ Λ + 6595 364 √ 1 − 4ν δ˜ Λ ◆ x6

• ν=µ/M

˜ Λ = 8 13  1 + 7ν − 31ν2 ✓ λ1 m5

1

+ λ2 m5

2

◆ + √ 1 − 4ν

• 1 + 9ν − 11ν2 ✓ λ1

m5

1

− λ2 m5

2

◆

x = (πMf)2/3

˜ Λ = λ m5

NS

weak EoS-dependence between many NS quantities, e.g.: “ I - Love - Q “ [moment of inertia, tidal Love number, rotational quadrupole]

NS binaries: merger frequency fpeak, post-merger spectrum

Approximate universality

25

[Read+2013] [Rezzolla&Takami 2016] [Yagi & Yunes 2013]

What to expect from aLIGO+Virgo

26

“standard” NS-NS event rate (40/yr), ~1 yr of data [some caveats with the analysis]: 𝝻 to ~10-50 %, radius to ~1-2 km, pressure to ~ factor of 2 [Lackey+2014] similar conclusions with hybrid NR waveforms [Shibata+2016] NS-BH systems: 𝝻/m5 to ~ 10-100 % [Lackey+ 2013]

[ Lackey+2014]

example results: λ example results: pressure

many caveats

Recent model improvement: dynamic tides

27

Ω

corresponds to the NS’s fundamental oscillation modes

QNS

eigenfrequency:

(internal structure - dependent) ωf ∼ p mNS/R3

R

tidal forcing frequency:

mΩ ∼ m p M/r3

NS’s response to the tidal field

0.01 0.02 0.03 0.04 0.05 0.06

• 0.1

0.1 0.2 0.3 21.6 13.6 10.4 8.6 7.5 6.6

• 0.1

H4 EoS, mNS=1.35M

` = 2

` = 3

k2

k3

∼

(mΩ)2 (mΩ)2−!2

f k`

• dyn. tides
• adiab. tides

λ` =

2(`−2) (2`−1)!!k`R2`+1

Love number

EOB Hamiltonian with tidal effects

28

A = App(M, ν, r) + λ`AAT(M, ν, r)

adiabatic tides (AT):

[Damour, Nagar, Bini+2009-2014]

𝞶

MAP

HEOB(r, pr, p, Q`m, P`m; M, ν, λ`, ωf)

ds2

eff = −Adt2 + Bdr2 + r2dφ2

good agreement with full evolution:

[TH+2016]

dynamic tides: effective description of from approximate solutions for QNS:

A = App(M, ν, r) + λeff

` (M, ν, r, λ`, ωf)AAT(M, ν, r)

0.01 0.02 0.03 0.04 0.05 0.06

• 0.1

0.1 0.2 0.3 21.6 13.6 10.4 8.6 7.5 6.6

• 0.1

` = 2 ` = 3

k2

k3

∼

(mΩ)2 (mΩ)2−!2

f k`

22 23 24 25 26

GW cycles

• 1.5
• 1
• 0.5

∆ φ22 [rad]

Performance of the tidal EOB model

29

BH-BH adiabatic tides NR error dynamic tides

nonspinng NS-BH mass ratio 2:1 𝚫=2 polytropic C=0.1444

1000 2000 3000

(t − r*)/M

• 0.2

0.0 0.2 Re(DLh22/M) Γ

EOB NR

22 23 24 25 26

GW cycles

• 1.5
• 1
• 0.5

∆ φ22 [rad]

Performance of the tidal EOB model

30

BH-BH adiabatic tides NR error dynamic tides

nonspinng NS-BH mass ratio 2:1 𝚫=2 polytropic C=0.1444

1000 2000 3000

(t − r*)/M

• 0.2

0.0 0.2 Re(DLh22/M) Γ

EOB NR

self-force adiabatic enhanced tidal EOB [Bernuzzi+]

Main imprint of NS microphysics in the GWs from inspirals: tidal effects Dynamic f-mode tides can be significant, now included in EOB Also included: NS-BH tidal disruption signal (nonspinning case) Further improve models and measurement potential, reduce systematics (inspiral, NS-BH tidal disruption, NS-NS merger/post-merger) Include more realistic physics Accurate NR simulations are crucial to inform model developments data analysis strategies (e.g. parameterization) connection with multimessenger signals

Conclusions

31

Outlook:

Thank you